Philip Seymour Hoffman’s longtime girlfriend was made preliminary executor of his estate Wednesday to begin the grim task of sorting out the late Oscar winner’s finances and moving his things from the rented apartment where he died.

Mimi O’Donnell – whom Hoffman named as executor in his 2004 will – was granted permission to make decisions for his estate while the will winds its way through Manhattan Surrogate’s Court.

Hoffman, who died of an apparent heroin overdose earlier this month, left his fortune to O’Donnell, the mother of their three kids, Cooper, 10, Tallulah, 7, and Willa, 5.

Court sources told The Post the family asked that his estate be handled by a judge on an expedited basis – a sign that the family needs cash.

In the court petition, O’Donnell said she needs access to Hoffman’s accounts to pay for funeral costs, outstanding bills and the rent on the Bethune Street apartment where the actor was found dead by friends Feb. 2, a hypodermic needle still stuck in his arm.

She estimated his net worth as “$500,000-plus” but did not provide any financial specifics.

Another document submitted by her lawyers Wednesday noted that O’Donnell and the kids “rely on [Hoffman’s] assets for their support.”

Hoffman’s wealth has been estimated at about $35 million by CelebrityNetWorth.com.

The filing noted that O’Donnell needs to “address pressing administrative matters” relating to Hoffman’s death, including “the need to unseal the apartment where the decedent was found dead,” the “need to protect and inventory assets including personal property” and “to retrieve personal effects being held by the NYC Police Dept.”

She also needs to make “prompt” investment and business decisions on behalf of the estate, and terminate Hoffman’s apartment lease.

Hoffman had been staying in his $10,000 a month bachelor pad, with O’Donnell and their kids living in the couple’s $4.2 million Jane Street apartment. Hoffman also owns a $1.4 million Sheridan Square penthouse, records show.

O’Donnell’s petition indicated that she doesn’t expect a challenge to the will, and probate is expected to be completed by June 18.

Hoffman’s daughters, who were not yet born when he wrote the will, are not named. But legal experts said the document contains language that provides for them under New York law.